With the milestone discovery of the Higgs boson at the CERN Large Hadron Collider (LHC), high energy physics has entered a new era. The completion of the “Standard Model” (SM) implies, for the first time ever, that we have a relativistic, quantum-mechanical, self-consistent theoretical framework, conceivably valid up to exponentially high energies, even to the Planck scale. Yet, the SM leaves many unanswered questions both from the theoretical and observational perspectives, including the nature of the electroweak superconductivity and its phase transition, the hierarchy between the particle masses and between the observed scales, the nature of dark matter etc. There are thus compelling reasons to believe that new physics beyond the SM exits, most likely associated with the electroweak symmetry breaking. The Energy Frontier and the Accelerator Frontier in the “Snowmass exercise” led by the APS DPF in the US identified the priority for an e+e- collider as a Higgs factory. We argue that the precision measurements at the Higgs factory and future high energy colliders would hold great promise to uncover the laws of nature to a deeper level.